Braun-Blanquet's legacy and data analysis in vegetation science

114 Podani, J. FORUM
on the most typical-looking plant or animal individuals.
Furthermore, when Braun-Blanquet developed his ideas
computers were not yet invented, sampling theory was
in an initial stage and the use of statistical methods in
biology was exceptional. As a result, the relevé method
is burdened by much bias, subjectivity, inconsistency,
arbitrariness, circular argumentation and large sampling
error (cf. Podani 1984 and references therein; Feoli
1984; Lepš & Hadincová 1992; Chytrý 2001; Chytrý &
Otypková 2003) – a peculiar combination of flaws probably
unprecedented in the natural sciences. We cannot
blame Braun-Blanquet, of course, that he was unable to
envisage all difficulties that were revealed only many
decades after the approach was launched. The problems
associated with sampling can be resolved by modernizing
and standardizing field methods, and there are
attempts in the contemporary literature to achieve this
goal (Bruelheide & Chytrý 2000; Mucina et al. 2000;
Chytrý & Otypková 2003; Grabherr et al. 2003). These
authors promote the use of various objective sampling
designs and standardized quadrat sizes which allow
generalizations to be made from relevé data.
Numerical syntaxonomy
Computers were introduced into the processing of
phytosociological data as early as the 1960s (cf. van der
Maarel 1975, 1982). Transition into the numerical phase
was greatly stimulated by the increased availability of
computer program packages and personal computers,
and the appearance of important books (e.g. Whittaker
1973; Orlóci 1978). Classification and ordination of
relevé data became an everyday practice of vegetation
scientists. The paradigm shift towards numerical analysis
was relatively straightforward, mostly because subjectivity,
inconsistency, and arbitrariness in selecting
the objects of the study play no direct role in multivariate
data exploration. Cluster analysis and ordination
impose no restrictions on sampling conditions: any set
of objects can be analysed provided that these are characterized
by an appropriate set of descriptors. Furthermore,
any dissimilarity matrix can be subjected to complete
linkage clustering or principal coordinates analysis,
for example, without violating any mathematical
rule. Of course, sampling methods need to be consistent
with the objectives of an investigation (see Kenkel et al.
1989 for a review of this topic). Classification and
ordination methods do have their own limitations, of
which compatibility of a procedure with the type of data
is of primary concern.
The issue of measurement scale
The basic source of computational problems is the
scale on which species performance is measured within
each relevé. Braun-Blanquet’s well-known abundance/
dominance scale is r, +, 1, 2, 3, 4 and 5, quite often
diluted with intermediate scores such as + - 1 or 1 - 2.
Obviously, the presence of non-numbers r and + in the
data immediately excludes the possibility of calculations,
therefore several procedures have been suggested
to convert the values to some other scale containing only
numerals (van der Maarel 1979).
These transformations overcome the non-number
problem, but the newly defined ‘ordinal scale’ preserves
a less apparent property: certain operations with the
values are strictly inadmissible (Anderberg 1973). Differences,
sums and ratios of possible values are not
interpretable on the ordinal scale, only the relations =
and < are meaningful, so that only the ordering of values
conveys information. In other words, the difference
between 1 and 2 is not the same as that between 3 and 4,
1+2 is not equal to 3 and 1/2 is not the same as 2/4. The
essence of the problem is that conventional dissimilarity
functions, clustering and ordination algorithms operate
via subtraction, addition and division and consequently
their application to relevé data is inappropriate.
It is striking that numerical syntaxonomic surveys
analysing Braun-Blanquet-type data completely disregard
this incompatibility, although there have been a
few reports recognizing this problem. Dale (1989), for
example, discussed the possibilities of calculating dissimilarity
based on ordinal abundance data, but his work
has been overlooked almost completely. The ISI database
includes only two references to this important paper,
while Google Scholar Search finds only one more document
– a painful indication of general ignorance.
At first glance, there appear to be several remedies.
At the level of sampling, one could record percentage
cover, biomass or counts of individuals, i.e., ‘quantitative
data’, so as to avoid all problems mentioned above.
But vegetation databases already include hundreds of
thousands of relevés most of which described in terms
of ordinal variables, and the joint evaluation of such
traditional data and quantitative data would be impossible.
Another solution is simplification of data to presence/absence
scores whose analysis poses no computational
problems. However, this implies information loss
because the ordinal scale variables tell us more about
interspecific relationships than simple presence and absence
data.
A further possibility is conversion of Braun-Blanquet
scores to mean values of percentage cover classes, but
the arbitrariness and the non-systematic distortion implied
in this operation are obvious. For example, if the